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URL: https://oeis.org/A076474

⇱ A076474 - OEIS

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A076474
Denominators of the slowest decreasing sequence of unit fractions whose partial sums have a prime numerator.
2
1, 2, 3, 5, 6, 10, 11, 13, 21, 23, 24, 29, 45, 48, 50, 51, 53, 54, 57, 58, 60, 68, 70, 81, 82, 98, 103, 104, 106, 120, 125, 128, 132, 139, 149, 164, 170, 192, 206, 214, 226, 228, 232, 235, 241, 257, 270, 275, 283, 305, 307, 314, 326, 351, 399, 412, 423, 436, 520
OFFSET
1,2
COMMENTS
By Dirichlet's Theorem, it is always possible to find the next term. See A076475 for the list of primes appearing in the numerator. Does this sum of unit fractions converge?
EXAMPLE
For example, 1/1 + 1/2 = 3/2, 1/1 + 1/2 + 1/3 = 11/6. However, 1/4 is not in the sequence because 1/1 + 1/2 + 1/3 + 1/4 = 25/12 and 25 is not prime.
MATHEMATICA
nMax = 100; lst = {1}; numer = {1}; s = 1; i = 2; Do[While[ ! PrimeQ[Numerator[s + 1/i]], i++ ]; s = s + 1/i; AppendTo[lst, i]; AppendTo[numer, Numerator[s]]; i++, {n, 2, nMax}]; lst
CROSSREFS
Cf. A076475.
Sequence in context: A316503 A316494 A178992 * A324968 A255059 A057760
KEYWORD
nonn,frac
AUTHOR
T. D. Noe, Oct 14 2002
STATUS
approved